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SUMMARY:Daniel Hu (Harvard)
DTSTART:20251204T213000Z
DTEND:20251204T230000Z
DTSTAMP:20260422T220451Z
UID:STAGE/145
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/145/">
 Local Monodromy</a>\nby Daniel Hu (Harvard) as part of STAGE\n\nLecture he
 ld in Room 2-105 in the MIT Simons Building.\n\nAbstract\nWe'll continue o
 ur discussion of Deligne's generalization of the Weil conjectures to the r
 elative setting. A theorem of Grothendieck allows us to define the monodro
 my operator on an ell-adic Galois representation that comes from cohomolog
 y of smooth proper varieties over local fields. This allows us to define a
  new filtration on H^i\, called the monodromy filtration. The monodromy-we
 ight conjecture states that it coincides with the weight filtration\, up t
 o a shift. We'll apply the case of function fields of curves to deduce the
  statement of Weil II.\n\nReference:\n\n1. Szamuely\, <a href = "https://p
 agine.dm.unipi.it/tamas/Weil.pdf"> A course on the Weil conjectures</a>\, 
 Section 7.6.\n\n2. Kiehl-Weissauer\, <a href = "https://link.springer.com/
 book/10.1007/978-3-662-04576-3"> Weil Conjectures\, Perverse Sheaves and $
 l$-adic Fourier Transform</a>\, Section I.3\, I.9.\n\n3. Deligne\, <a href
  = "https://link.springer.com/content/pdf/10.1007/BF02684780.pdf"> La conj
 ecture de Weil. II</a>\, 1.3\, 1.7\, 1.8?\n
LOCATION:https://researchseminars.org/talk/STAGE/145/
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